The cell cycle is the process by which a growing cell replicates its genome and partitions the two copies of each chromosome to two daughter cells at division. It is of utmost importance to the perpetuation of life that these processes of replication (DNA synthesis) and partitioning (mitosis) be carried out with great fidelity. In eukaryotic cells, DNA synthesis (S phase) and mitosis (M phase) are separated in time by two gaps (G1 and G2). Proper alternation of S phase and M phase is enforced by `checkpoints' that block progression through the cell cycle if the genomic integrity of the cell is compromised in any way. For example, if DNA is damaged in G1 phase a checkpoint blocks progression into S phase until the damage can be repaired. If replicated chromosomes are not properly aligned on the mitotic spindle, a different checkpoint blocks progression into anaphase (the phase of sister chromatid separation) until all sister chromatids are properly attached to opposite poles of the spindle. Checkpoints are able to block cell cycle progression by sending a STOP signal to the molecular mechanisms that govern specific cell-cycle transitions (G1-S, G2-M, and M-G1). The molecular mechanisms that govern each of these transitions have a peculiar property called `bistability.' Under physiological conditions, the control mechanism can persist indefinitely in either of two characteristic states: the OFF state, which corresponds to holding the cell cycle in the pre-transition phase; and the ON state, which corresponds to pushing the cell cycle into the post-transition phase. Checkpoint STOP signals seem to act by stabilizing the appropriate bistable switches in its OFF state. Because these checkpoints are crucial to maintaining the integrity of an organism's genome from one generation of cells to the next, it is vital that they function reliably even in the face of random molecular fluctuations that are inevitable in a cell a small as a yeast cell (30 fL). Calculations based on stochastic models of the molecular mechanisms governing cell cycle progression suggest that checkpoint functions are indeed robust in wild-type budding yeast cells, but they may be compromised in strains carrying mutations of specific checkpoint genes. The purpose of this proposal is to provide the mathematical models and experimental data needed to understand how cell cycle checkpoints operate reliably in wild-type yeast cells and how they fail in mutant cells. To reach this goal wil require new advances in stochastic modeling and in the technology of measuring mRNA and protein molecules in single yeast cells. To test the models will require the expertise to construct and characterize the phenotypes of specific mutant strains of budding yeast that are predicted by the model to exhibit fragility of checkpoint arrest in the face of random fluctuations in yeast mRNAs and proteins. Because all eukaryotic organisms seem to employ the same fundamental molecular machinery that governs progression through the cell division cycle, the understanding of checkpoint operations in yeast cells will translate into a better understanding of checkpoint functions and failures in other types of cells, most notably human cells.